"X as a Service" is a common enough term that someone is more likely to have heard it before, and it accurately describes what it is (if the X is accurate).

"Serverless" is deliberately wrong and misleading.

One of those stupid "entire website in a page" would be a better fit for "server less" because technically the logic is all client side.

At least it's clear that it depends on a service, with all that entails.